Three-Dimensional SCFTs, Supersymmetric Domain Wall and Renormalization Group Flow

TL;DR

This paper explores the renormalization group flow in a three-dimensional superconformal field theory derived from gauged N=8 supergravity, identifying fixed points and constructing domain wall solutions that preserve supersymmetry.

Contribution

It explicitly constructs the scalar field configurations and superpotential in gauged N=8 supergravity, linking them to RG flow and supersymmetric domain wall solutions.

Findings

Identified RG flow from N=8 to N=2 fixed point.

Constructed explicit scalar field configurations and superpotential.

Numerical analysis of flow equations between critical points.

Abstract

By analyzing SU(3)xU(1) invariant stationary point, studied earlier by Nicolai and Warner, of gauged N=8 supergravity, we find that the deformation of S^7 gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N=8, SO(8) invariant UV fixed point to N=2, SU(3)xU(1) invariant IR fixed point. By explicitly constructing 28-beins u, v fields, that are an element of fundamental 56-dimensional representation of E_7, in terms of scalar and pseudo-scalar fields of gauged N=8 supergravity, we get A_1, A_2 tensors. Then we identify one of the eigenvalues of A_1 tensor with ``superpotential'' of de Wit-Nicolai scalar potential and discuss four-dimensional supergravity description of renormalization group flow, i.e. the BPS domain wall solutions which are equivalent to vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving bosonic background of gauged N=8 supergravity. A numerical analysis of the steepest descent equations interpolating two critical points is given.